Vasile Staicu

Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints

Introduction Mathematical background Degree theoretic results Variational-hemivariational inequalities Hemivariational inequalities with an asymmetric subdifferential Bibliography.

The Bellman Equation for Time-Optimal Control of Noncontrollable, Nonlinear Systems

AbstractFor a general nonlinear system and closed target set ℐ we study the value functionsν and

Nodal solutions for

\hat \upsilon

-equations

of the control problems of reaching ℐ and, respectively, its interior, in minimum time. Under no controllability assumptions on the system, we characterize them as, respectively, the minimal viscosity supersolution and the maximal viscosity subsolution of the Bellman equation with appropriate boundary conditions. Then we prove that

On a

\hat \upsilon

-superlinear Neumann

is the unique upper semicontinuous ‘complete solution’ of such a boundary value problem, which means in particular that the (completed) graph of